In medicine, ultrasound probes such as the one shown in Figure \ref{fig:ultrasound_probe} are used to obtain 2D ultrasound scans called \emph{bscans}. The probe both emits ultrasound pulses and detects their echo back. As the ultrasound pulse travels through tissue, echoes are created when it encounters materials with varying density. In most cases, not all of the pulse energy is absorbed, and so the pulse continues forward.

	\begin{figure}[h]
	\centering
	\includegraphics[height=0.3\textheight]{graphics/ultrasound_probe.png}
	\caption{Ultrasound probe}
	\label{fig:ultrasound_probe}
	\end{figure}

The speed of sound depends on the transmission material, but one can assume constant speed $v = 1540$ $m/s$ in human tissue. This means that the distance $d$ from the transducer to the density variation can be estimated by the time $t$ it took for the echo to arrive at the transducer:

	\begin{equation}
		d = \frac{vt}{2}
		\label{eq:ultrasound_distance}
	\end{equation}
	
The strength of the echo is given by the difference between acoustic impedances of the materials next to each other. If the probe emmits and receives ultrasound in a linear array, a 2D image can be formed where the height is the distance from the probe, the width is the width of the array and the intensity of a pixel is the strength of the echo. This image is the ultrasound bscan. The array can also be curved, giving a fan shaped bscan. Examples of linear and fan shaped bscan are shown in Figure \ref{fig:bscan_examples}.

	\begin{figure}[h]
	\centering
	\includegraphics[width=0.4\textwidth]{graphics/linear_bscan.png}
	\includegraphics[width=0.4\textwidth]{graphics/fan_bscan.png}
	\caption{Linear and fan shaped bscan}
	\label{fig:bscan_examples}
	\end{figure}

To construct a 3D volume, each bscan is tagged with a timestamp and location and rotation of the probe in space. This data is then processed, which can take minutes to hours depending on the quality of the reconstruction. There are several ways to obtain the orientation (location and rotation) of the probe. Some approaches include attaching the probe to mechanical structures with certain degrees of freedom or letting a machine move the probe in sweeps. More practical is to move the probe by freehand and track its location by an optical tracking system as shown in Figure \ref{fig:tracking_system}. This is the method used for the data obtained in this thesis. Spheres that reflect infrared light are attached to the probe, and two cameras record the reflected infrared light. The position of the spheres relative to the cameras is used to estimate the location and orientation of the probe.

	\begin{figure}[h]
	\centering
	\includegraphics[width=\textwidth]{graphics/tracking_system.png}
	\caption{Probe with tracking equipment and infrared cameras}
	\label{fig:tracking_system}
	\end{figure}